What is the integral from 1 to infinity of 1/(x^5) ?

The integral from 1 to infinity of 1/(x^5) is 1/4

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integral from 1 to infinity of 1/(x^5)

\int_{1}^{\infty} \frac{1}{x ^{5}} d x

\frac{1}{4}

Solution steps

\int_{1}^{\infty} \frac{1}{x ^{5}} d x

Compute the indefinite integral:

\int \frac{1}{x ^{5}} d x = - \frac{1}{4 x ^{4}} + C

Compute the boundaries:

\int_{1}^{\infty} \frac{1}{x ^{5}} d x = 0 - (- \frac{1}{4})

= 0 - (- \frac{1}{4})

Simplify

= \frac{1}{4}

\int \frac{ln ( 8 x )}{x} d x

\frac{d}{d x} (\frac{1}{( 1 + x ^{2} ) 1 + x ^{2}})

\frac{d}{d x} (sin (x) + \frac{4}{9} cot (x))

x \to 1 lim (F (x))

What is the integral from 1 to infinity of 1/(x^5) ?
The integral from 1 to infinity of 1/(x^5) is 1/4